Abstract
Can machines think? Since Alan Turing asked this question in 1950, nobody is
able to give a direct answer, due to the lack of solid mathematical foundations
for general intelligence. In this paper, we introduce a categorical framework
towards this goal, consisting of four components: the sensor, world category,
planner with objectives, and actor. By leveraging category theory, many
important notions in general intelligence can be rigorously defined and
analyzed. For instance, we introduce the concept of self-state awareness as a
categorical analogy for self-consciousness and provide algorithms for learning
and evaluating it. For communication with other agents, we propose to use
diagrams that capture the exact representation of the context, instead of using
natural languages. Additionally, we demonstrate that by designing the
objectives as the output of function over self-state, the model's
human-friendliness is guaranteed. Most importantly, our framework naturally
introduces various constraints based on categorical invariance that can serve
as the alignment signals for training a model that fits into the framework.
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